A construction method for a scale-related ocean island distribution function model

Abstract

The present invention relates to the technical field of function model algorithms, and specifically discloses a method for constructing a scale-related ocean island distribution function model, including the following steps: Step 1: Use a fractal function to simulate a fractal contour to obtain a continuous fractal island contour; Step 2: Obtain all island diameters l1, l2, l3 ··· l intercepted on a sea level with a height of h0. n , as the interception of the island contour is different, if a situation different from other cases is obtained where the left and right intersection points are not in one-to-one correspondence in order, a simple judgment and arrangement are required to obtain all island diameters. Statistic all the obtained island diameters to obtain the relationship between the number and diameter; Step 3: Obtain the diameter-number relationship formula and take the logarithm of both sides of the function; Step 4: Observe the influence of the fractal dimension D on several groups of B and λ; Step 5: Obtain the ocean island distribution function relationship formula. It can calculate the number of ocean islands more accurately, and then predict the area of ocean islands more accurately.

Description

Technical Field

[0001] The present invention relates to the technical field of function model algorithms, and specifically to a construction method of a scale-related ocean island distribution function model. Background Art

[0002] The ocean island distribution function is a key function for establishing a fractal contact model. The existing ocean island distribution function is scale-independent, which will result in the same contact mechanical properties of fractal surfaces with different scales and different topographies. Summary of the Invention

[0003] In view of the problems existing in the prior art, the present invention proposes a construction method of a scale-related ocean island distribution function model, which can truly reflect the contact mechanical properties of the fractal surface and embody the internal relationship between the scale of the fractal surface, the surface topography parameters and the contact mechanical properties.

[0004] A construction method of a scale-related ocean island distribution function model of the present invention includes the following steps:

[0005] Step 1: Use a fractal function to simulate the fractal contour. First, arbitrarily specify a sampling length L, take a sufficient number of points, and obtain the function values of the corresponding points. However, at this time, they are discrete points and do not resemble a complete island contour. Therefore, interpolation is performed between adjacent points to obtain a continuous fractal island contour;

[0006] Step 2: Assume that the maximum height of the fractal contour is h, and take a horizontal line with a height of h0 to simulate the sea level. The sea level height satisfies 0 < h0 < h. The intersection of the sea level and the island contour yields several intersection points, which are represented by x0, x1, x2...x n ; If the island is regarded as a superimposed sine wave, any intersection point is defined as the left intersection point or the right intersection point of a wave crest. According to the positive or negative slope at the intersection point, if it is positive, the point is the left intersection point; otherwise, it is the right intersection point. x0 and x1 are the left and right intersection points of a wave crest. The difference between the abscissas of the right intersection point and the left intersection point gives the island diameter l1. By analogy, all the island diameters l1, l2, l3...l intercepted on the sea level with a height of h0 are obtained. n As the interception of the island contour is different, if it is obtained that, different from other cases, the left and right intersection points are not in one-to-one correspondence in sequence, a simple judgment and arrangement are required to obtain all the island diameters. The statistics of all the obtained island diameters yield the relationship between the quantity and the diameter;

[0007] Step 3: Obtain the diameter - quantity relationship formula, take the logarithm of both sides of the function, and obtain

[0008]

[0009] where N is the number of intercepted islands, l is the size of the island, lmax is the island with the largest size, and B and λ are parameters to be determined;

[0010] According to the relationship of lnN - ln(l max / l) for fitting, the slope of the data points is the exponent B, and the coefficient λ calculated by substituting into the numerical relationship; Repeat the experiment, divide the island height into several parts, continue to change the sea level height, and make the sea level traverse each island height, and finally obtain several sets of values of B and λ, and observe the change trend of B and λ;

[0011] Step 4: Change the fractal dimension D, repeat the above steps 2 and 3, and observe the influence of the fractal dimension D on several sets of B and λ; Change the sampling length L and repeat the above steps 2 and 3 to verify the influence of the sampling length L on B and λ, and finally obtain the change law of the parameters B and λ;

[0012] Step 5: After the above steps, combine the influences of the parameter sampling length L, fractal dimension D, and truncation height h on the ocean island distribution function, and finally obtain the relational expression of the ocean island distribution function.

[0013] Preferably, in the above step 1, the fractal contour simulation includes the following steps:

[0014] Step 1.1: Simulate the fractal contour through a fractal function;

[0015]

[0016] where G is the scale parameter, D is the fractal dimension, n min is the minimum frequency exponent, n max is the maximum frequency exponent, γ represents the contour spatial frequency, x is the independent variable, and z(x) represents the contour height;

[0017] Step 1.2: Simulate the fractal contour through Fourier transform;

[0018]

[0019] In formula (3), N is the number of sampling points, k and x represent the sampling point numbers in the frequency domain and the real domain, R m (k) is a random number on 0 to 1, R(k) is the complex number corresponding to R m (k), i is the imaginary unit, θ is an arbitrary angle, s(ω) is the power spectral density function, C is the scale coefficient, D is the fractal dimension, ω is the frequency in the power spectrum, z represents the contour height, and B(k) is the arithmetic square root of the power spectral density;

[0020] Step 1.3: Obtain the fractal contour by experimentally observing the specimen;

[0021] The surface of the specimen was observed using a Leica microscope. Through data statistics and processing, the fractal contour of the specimen surface was obtained. According to the fractal contour, the contour fractal dimension was measured using the structure function method:

[0022] S(τ) = <[z(x + τ) - z(x)] 2 > = cτ 4-2D (4);

[0023] In Equation (4), S(τ) is the arithmetic mean of the squared differences, z(x) represents the contour height, c is a constant, τ is a random value of the data interval. The relationship between the slope β and the fractal dimension D is obtained by fitting the S(τ) - τ relationship:

[0024] D = 2 - β / 2 (5).

[0025] Preferably, in step 2, the steps to obtain parameters B and λ according to different fractal contours are as follows:

[0026] Step 2.1: Obtain parameters B and λ according to the fractal function;

[0027] According to the algorithm, the number - diameter relationship is obtained, and the value of parameter B is obtained by fitting the data through the algorithm;

[0028] According to the algorithm, the values of parameter λ at different heights are obtained, and at the same time, the values of parameter λ are calculated by taking different sampling lengths;

[0029] The above results are obtained through algorithm calculation, and then parameters B and λ are obtained, as shown in Equations (6) and (7):

[0030]

[0031] In Equation (6), B is the parameter to be determined, D represents the fractal dimension, h is the truncation height, h0 represents the maximum distance of the island from the average height, l max represents the maximum island diameter, and l represents the island diameter;

[0032] According to Equation (6), parameter B is jointly determined by the fractal dimension D and the truncation height h;

[0033]

[0034] In Equation (7), λ is the parameter to be determined, L represents the sampling length, L0 is the reference sampling length, h is the truncation height, and h0 represents the maximum distance of the island from the average height;

[0035] According to Equation (7), parameter λ is jointly determined by the sampling length L and the truncation height h:

[0036] The variation law of l max was obtained through numerical fitting, as shown in Equation (8):

[0037]

[0038] Equation (8) l max represents the maximum diameter of the ocean island, L0 is the reference sampling length, h is the truncation height, h0 represents the maximum distance of the ocean island from the average height, D is the fractal dimension, and a and b are parameters related to the fractal dimension;

[0039] Therefore, the ocean island distribution function obtained from the WM function is:

[0040]

[0041] In Equation (9), N is the number of ocean islands, and Λ is all ocean islands with a diameter greater than a certain ocean island;

[0042] Step 2.2: Parameters B and λ obtained according to the Fourier transform;

[0043] According to the algorithm, the value of parameter B is obtained, and at the same time, the value of parameter λ is obtained;

[0044] The above results are calculated by the algorithm to obtain parameters B and λ, as shown in Equations (10) and (11):

[0045]

[0046] In Equation (10), B is the parameter to be solved;

[0047] According to Equation (10), parameter B is jointly determined by the fractal dimension D and the truncation height h

[0048]

[0049] In Equation (11), λ is the parameter to be solved;

[0050] According to Equation (11), parameter λ is determined by the truncation height h, and the change law of l max is obtained through numerical fitting, as shown in Equation (12):

[0051]

[0052] Therefore, the ocean island distribution function obtained by the Fourier transform method is:

[0053]

[0054] Step 2.3: Parameters B and λ obtained according to the experimental measurement of the fractal profile;

[0055] According to the algorithm, the value of parameter B is obtained, and at the same time, the value of parameter λ is calculated:

[0056] The value of parameter λ at different sampling lengths is obtained according to the algorithm;

[0057] The above results are obtained through algorithm calculation to get parameters B and λ, as shown in Equations (14) and (15):

[0058]

[0059] It is found from Equation (14) that parameter B is jointly determined by the fractal dimension D and the cut-off height h

[0060]

[0061] In Equation (15), Ra is the roughness;

[0062] It is found from Equation (15) that parameter λ is jointly determined by the sampling length L and the cut-off height h;

[0063] The variation law of l max is obtained by numerical fitting, as shown in Equation (16), where the roughness Ra is obtained according to actual measurement:

[0064]

[0065] Therefore, the ocean island distribution function obtained from the real machining surface is obtained;

[0066]

[0067] A new scale-related ocean island distribution function is obtained through the fractal profiles of theoretical and actual measurement of machined specimens:

[0068]

[0069] In Equation (18), F(L) is a function of the sampling length L, K(h / h0) is a function of h and h0, D is the fractal dimension, is a function of h and h0, and ξ(l) is a function of the cut-off length;

[0070] It can be seen from the above formula that for common fractal profiles, the ocean island distribution function has a unified structural form. In the formula, F(L) is the sampling length function, which is scale-related and proportional to the sampling length. For the fractal profile simulated by the WM function, F(L) = L / L0; for the fractal profile simulated by the Fourier transform, F(L) = 1; for the machined surface, F(L) = 1.12L / (100Ra). K(h / h0) is the cut-off height function, showing a parabolic law with the cut-off height. For the fractal profile simulated by the WM function, K(h / h0) = 10 + 0.15(h / h0) - 11(h / h0) 2; For the fractal profile simulated by Fourier transform, K(h / h0) = 6.8 + 0.15(h / h0) - 6.54(h / h0) 2 ; For machined surfaces, K(h / h0) = 8 - 0.5(h / h0) - 10(h / h0) 2 . is the exponential truncation height function. For the fractal profile simulated by the WM function For the fractal profile simulated by Fourier transform For machined surfaces ξ(l) is the truncation length function. For the fractal profile simulated by the WM function, ξ(l) = 0.12(l max - l) / l max ; For the fractal profile simulated by Fourier transform, ξ(l) = 0.15(l max - l) / l max ; For machined surfaces, ξ(l) = 0.18(l max - l) / l max .

[0071] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0072] The present invention takes into account the scale correlation and the influence of different sea level heights on the ocean island distribution function, and obtains a new scale-dependent ocean island distribution function, which can calculate the number of ocean islands more accurately, and thus predict the area of ocean islands more accurately. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] Figure 1 is a simplified schematic diagram of the island contour of the present invention;

[0074] Figure 2 is the fractal profile simulated by the Fourier transform method of the present invention;

[0075] Figure 3 is the fractal profile of different fractal dimensions by the experimental method of the present invention;

[0076] Figure 4 is the fractal profile corresponding to different sampling lengths of the experiment of the present invention;

[0077] Figure 5 is the influence of different truncation heights of the WM function of the present invention on the number-diameter relationship;

[0078] Figure 6 is the influence of different fractal dimensions in the WM function of the present invention on the parameter B;

[0079] Figure 7 is the influence of different fractal dimensions in the WM function of the present invention on the parameter λ;

[0080] Figure 8 For the influence of different sampling lengths on the parameter λ in the WM function of the present invention;

[0081] Figure 9 For the influence of different fractal dimensions on the parameter B in the Fourier transform method of the present invention;

[0082] Figure 10 For the influence of different fractal dimensions on the parameter λ in the Fourier transform method of the present invention;

[0083] Figure 11 For the influence of different fractal dimensions on the parameter B in the experimental method of the present invention;

[0084] Figure 12 For the influence of different fractal dimensions on the parameter λ in the experimental method of the present invention;

[0085] Figure 13 For the influence of different sampling lengths on the parameter λ in the experimental method of the present invention. Detailed implementation manners

[0086] The following will disclose multiple implementation manners of the present invention through illustrations. For the sake of clear description, many physical details will be described together in the following narrative. However, it should be understood that these physical details are not used to limit the present invention. That is to say, in some implementation manners of the present invention, these physical details are unnecessary. In addition, for the sake of simplifying the illustrations, some conventional structures and components will be shown in a simple schematic manner in the illustrations.

[0087] In addition, the technical solutions between various embodiments can be combined with each other, but it must be based on what can be achieved by those of ordinary skill in the art. When the combination of technical solutions conflicts with each other or cannot be achieved, it should be considered that such a combination of technical solutions does not exist and is not within the protection scope required by the present invention.

[0088] 1 Fractal contour simulation

[0089] 1.1 Simulating the fractal contour through the fractal function

[0090]

[0091] where G is the scale parameter, D is the fractal dimension, n min is the minimum frequency index, n max is the maximum frequency index, γ represents the contour spatial frequency, x is the independent variable, and z(x) represents the contour height;

[0092] Table 1 A set of parameters for generating the fractal contour by the WM function

[0093] Parameter <![CDATA[n min > <![CDATA[n max > G D γ Value range 1～10 30～50 5e-8 to 5e-16 1.1～1.9 1.5

[0094] Select according to formula (2) and the parameter range in Table 1 as needed to simulate an ideal fractal profile;

[0095] 1.2 Simulate the fractal profile through Fourier transform;

[0096]

[0097] In formula (3), N is the number of sampling points, k and x represent the sampling point numbers in the frequency domain and the real domain, R m (k) is a random number between 0 and 1, R(k) is the complex number corresponding to R m (k), i is the imaginary unit, θ is an arbitrary angle, s(ω) is the power spectral density function, C is the scale coefficient, D is the fractal dimension, ω is the frequency in the power spectrum, z represents the profile height, and B(k) is the arithmetic square root of the power spectral density;

[0098] Table 2 A set of parameters for generating a fractal profile by the Fourier transform method

[0099] Parameter N <![CDATA[R m > θ D C Value range <![CDATA[2 12～15 > Pseudo-random number between 0 and 1 π / 4～π / 3 1.1～1.9 1e-1 to 1e3

[0100] Select according to formula (3) and the data range in Table 2 as needed to simulate an ideal fractal profile, as shown in Figure (2):

[0101] 1.3 Obtain the fractal profile by experimentally observing the specimen;

[0102] Use a Leica microscope to observe the surface of the specimen. Through data statistics and processing, obtain the fractal profile of the specimen surface. According to the fractal profile, measure the profile fractal dimension using the structure function method

[0103] S(τ) = <[z(x + τ) - z(x)] 2 > = cτ 4-2D (4);

[0104] In formula (4), S(τ) is the arithmetic mean of the squared differences, z(x) represents the profile height, c is a constant, τ is a random value of the data interval, and the relationship between the slope β and the fractal dimension D is obtained by fitting the S(τ)-τ relationship:

[0105] The relationship between the slope β and the fractal dimension D is obtained by fitting the S(τ)-τ relationship:

[0106] D = 2 - β / 2 (5);

[0107] As shown in Figure (3) and Figure (4), the experimental profiles 2 with different fractal dimensions and different sampling lengths are shown. Obtain the parameters B and λ according to different fractal profiles;

[0108] 2.1 The parameters B and λ obtained according to the WM function;

[0109] The relationship between quantity and diameter is obtained according to the algorithm, as shown in Fig. (5). The value of parameter B is obtained by fitting the data through the algorithm, as shown in Fig. (6):

[0110] The value of parameter λ at different heights is obtained according to the algorithm, as shown in Fig. (7). At the same time, by taking different sampling lengths, the value of parameter λ can be calculated, as shown in Fig. (8):

[0111] The above results are obtained through algorithm calculation, and then parameters B and λ are obtained, as shown in Eqs. (6) and (7):

[0112]

[0113] In Eq. (6), B is the parameter to be determined, D represents the fractal dimension, h is the truncation height, h0 represents the maximum distance of the island from the average height, l max represents the maximum island diameter, and l represents the island diameter;

[0114] According to Eq. (6), parameter B is jointly determined by the fractal dimension D and the truncation height h

[0115]

[0116] In Eq. (7), λ is the parameter to be determined, L represents the sampling length, L0 is the reference sampling length, h is the truncation height, and h0 represents the maximum distance of the island from the average height;

[0117] According to Eq. (7), parameter λ is jointly determined by the sampling length L and the truncation height h;

[0118] The variation law of l max is obtained through numerical fitting, as shown in Eq. (8):

[0119]

[0120] In Eq. (8), l max represents the maximum island diameter, L0 is the reference sampling length, h is the truncation height, h0 represents the maximum distance of the island from the average height, D is the fractal dimension, and a and b are parameters related to the fractal dimension;

[0121] Therefore, the ocean island distribution function obtained from the WM function is obtained:

[0122]

[0123] In Eq. (9), N is the number of ocean islands, Λ is all islands with a diameter greater than a certain island diameter, l represents the island diameter, l max represents the maximum island diameter, L is the sampling length, L0 is the reference sampling length, h is the truncation height, h0 represents the maximum distance of the island from the average height, and D is the fractal dimension;

[0124] 2.2 Parameters B and λ obtained according to the Fourier transform:

[0125] The value of parameter B is obtained according to the algorithm, as shown in Fig. (9), and at the same time, the value of parameter λ is obtained, as shown in Fig. (10):

[0126] The above results of parameters B and λ are obtained through algorithm calculation, as shown in Equations (10) and (11)

[0127]

[0128] In Equation (10), B is the parameter to be determined, D represents the fractal dimension, h is the truncation height, h0 represents the maximum distance of the island from the average height, l max represents the maximum island diameter, and l represents the island diameter;

[0129] According to Equation (10), the parameter B is determined jointly by the fractal dimension D and the truncation height h

[0130]

[0131] In Equation (11), λ is the parameter to be determined, h is the truncation height, and h0 represents the maximum distance of the island from the average height;

[0132] According to Equation (11), the parameter λ is determined by the truncation height h, and the variation law of l max is obtained through numerical fitting, as shown in (12):

[0133]

[0134] In Equation (12), l max represents the maximum island diameter, L0 is the reference sampling length, h is the truncation height, h0 represents the maximum distance of the island from the average height, D is the fractal dimension, and a and b are parameters related to the fractal dimension;

[0135] Therefore, the ocean island distribution function obtained by the Fourier transform method is obtained

[0136]

[0137] In Equation (13), N is the number of ocean islands, Λ is all islands with a diameter greater than a certain island diameter, l represents the island diameter, and l max represents the maximum island diameter, h is the truncation height, h0 represents the maximum distance of the island from the average height, and D is the fractal dimension;

[0138] 2.3 Parameters B and λ obtained according to the experimental measurement of the fractal profile;

[0139] The value of parameter B is obtained according to the algorithm, as shown in Fig. (11). At the same time, the value of parameter λ is calculated, as shown in Fig. (12):

[0140] The values of parameter λ under different sampling lengths are obtained according to the algorithm, as shown in Fig. (13)

[0141] The above results are calculated by the algorithm to obtain parameters B and λ, as shown in Eqs. (14) and (15):

[0142]

[0143] In Eq. (14), B is the parameter to be solved, D represents the fractal dimension, h is the truncation height, h0 represents the maximum distance of the island from the average height, l max represents the maximum island diameter, and l represents the island diameter;

[0144] It is found from Eq. (14) that parameter B is jointly determined by the fractal dimension D and the truncation height h

[0145]

[0146] In Eq. (15), λ is the parameter to be solved, L represents the sampling length, Ra is the roughness, h is the truncation height, and h0 represents the maximum distance of the island from the average height;

[0147] It is found from Eq. (15) that parameter λ is jointly determined by the sampling length L and the truncation height h

[0148] The variation law of l max is obtained by numerical fitting, as shown in Eq. (16), where the roughness Ra is obtained from actual measurement:

[0149]

[0150] In Eq. (16), l max represents the maximum island diameter, Ra is the roughness, h is the truncation height, h0 represents the maximum distance of the island from the average height, D is the fractal dimension, and a and b are parameters related to the fractal dimension;

[0151] Therefore, the ocean island distribution function obtained from the real machining surface is obtained;

[0152]

[0153] In Eq. (17), N is the number of ocean islands, Λ is all islands with a diameter greater than a certain island diameter, l represents the island diameter, and l max represents the maximum island diameter, L is the sampling length, Ra is the roughness, h is the truncation height, h0 represents the maximum distance of the island from the average height, and D is the fractal dimension;

[0154] 3 Conclusion:

[0155] A new scale - related ocean island distribution function is obtained by the fractal profiles of theoretical and actual measured machined specimens.

[0156]

[0157] In Equation (18), N is the number of ocean islands, Λ is all the islands larger than a certain island diameter, l represents the island diameter, l max represents the maximum island diameter, F(L) is a function of the sampling length L, h is the truncation height, h0 represents the maximum distance of the island from the average height, K(h / h0) is a function of h and h0, D is the fractal dimension, is a function of h and h0, and ξ(l) is a function of the truncation length;

[0158] It can be seen from the above formula that for common fractal profiles, the ocean island distribution function has a unified structural form. In the formula, F(L) is the sampling length function, which is scale - related and proportional to the sampling length. For the fractal profile simulated by the WM function, F(L)=L / L0; for the fractal profile simulated by the Fourier transform, F(L)=1; for the machined surface, F(L)=1.12L / (100Ra). K(h / h0) is the truncation height function, showing a parabolic law with the truncation height. For the fractal profile simulated by the WM function, K(h / h0)=10 + 0.15(h / h0)-11(h / h0) 2 ; for the fractal profile simulated by the Fourier transform, K(h / h0)=6.8 + 0.15(h / h0)-6.54(h / h0) 2 ; for the machined surface, K(h / h0)=8 - 0.5(h / h0)-10(h / h0) 2 . is the exponential truncation height function. For the fractal profile simulated by the WM function For the fractal profile simulated by the Fourier transform, For the machined surface, ξ(l) is the truncation length function. For the fractal profile simulated by the WM function, ξ(l)=0.12(l max -l) / l max ; for the fractal profile simulated by the Fourier transform, ξ(l)=0.15(l max -l) / l max ; for the machined surface, ξ(l)=0.18(l max -l) / l max . The detailed parameters are shown in Table 3 below:

[0159] Table 3 Parameter Table of Ocean Island Distribution Function

[0160]

[0161] The above are only the embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various changes and modifications. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the scope of the claims of the present invention.

Claims

1. A method for constructing a scale-dependent ocean island distribution function model, characterized in that: The steps include: Step 1: Use fractal function to simulate fractal contour. First, arbitrarily give a sampling length L, take enough points, and get the function value of the corresponding point. However, these points are discrete and not like a complete island contour. Therefore, interpolation is performed between two adjacent points to get a continuous fractal island contour. Step 2: Assume that the maximum height of the fractal outline is h, take a horizontal line with a height of h0 to simulate the sea level. The sea level satisfies 0<h0<h. The sea level intersects with the island outline to obtain several intersection points. The intersection points are denoted by x0, x1, x2…x n Indicates that if the island is regarded as a superimposed sine wave, any intersection point is defined as the left intersection point or right intersection point of a wave crest. The slope at the intersection point is positive or negative. If it is positive, then the point is the left intersection point, otherwise it is the right intersection point. x0 and x1 are the left and right intersection points of a wave crest. The difference between the horizontal coordinates of the right intersection point and the left intersection point is the island diameter l1. By analogy, the diameters of all islands intercepted at the sea level with a height of h0 are obtained: l1, l2, l3…l n , as the island outline is intercepted differently, if the result is different from other cases, the left and right intersection points are not in order one by one, and a simple judgment and arrangement is required to obtain the diameters of all islands, and then the diameters of all the islands obtained are counted to obtain the diameter-quantity relationship; Step 3: Get the diameter-number relationship, take the logarithm of both sides of the function, and get Where N is the number of intercepted islands, l is the size of the island, and l max is the size of the largest island, B and λ are parameters to be determined; According to lnN-ln(l max / l), the slope of the data point is exponent B, and the coefficient λ is substituted into the numerical relationship to obtain the calculated coefficient λ; repeat the experiment, divide the island height into several parts, continue to change the sea level height, so that the sea level traverses each island height, and obtain several groups of B and λ values, and observe the change trend of B and λ; Step 4: Change the fractal dimension D, repeat the above steps 2 and 3, and observe the influence of the fractal dimension D on several groups of B and λ; change the sampling length L and repeat the above steps 2 and 3 to verify the influence of the sampling length L on B and λ, and finally obtain the change law of the parameters B and λ; Step 5: After the above steps, combined with the influence of parameters such as sampling length L, fractal dimension D, and cutoff height h on the ocean island distribution function, the ocean island distribution function relationship is finally obtained.

2. The method for constructing a scale-dependent ocean island distribution function model according to claim 1, characterized in that: In step 1, the fractal contour simulation includes the following steps: Step 1.1: Simulate fractal contours through fractal functions; Where G is the scale parameter, D is the fractal dimension, and n min is the minimum frequency index, n max is the maximum frequency index, γ represents the spatial frequency of the profile, x is the independent variable, and z(x) represents the profile height; Step 1.2: Simulate fractal contours through Fourier transform; In formula (3), N is the number of sampling points, k and x represent the sampling point numbers in the frequency domain and real domain, and R m (k) is a random number between 0 and 1, R(k) is R m (k) is the complex number corresponding to, i is the imaginary unit, θ is an arbitrary angle, s(ω) is the power spectral density function, C is the scale factor, D is the fractal dimension, ω is the frequency in the power spectrum, z represents the profile height, and B(k) is the arithmetic square root of the power spectral density; Step 1.3: Obtain fractal contours by experimentally observing the test piece; The surface of the specimen was observed using a Leica microscope. The fractal profile of the specimen surface was obtained through data statistics and processing. Based on the fractal profile, the fractal dimension of the profile was measured using the structure function method: S(τ)=<[z(x+τ)-z(x)] 2 >=cτ 4-2D (4); In formula (4), S(τ) is the arithmetic mean of the square of the difference, z(x) represents the contour height, c is a constant, and τ is a random value of the data interval. By fitting the data S(τ)-τ relationship, the relationship between the slope β and the fractal dimension D is obtained: D＝2-β / 2 (5)。 3. The method for constructing a scale-dependent ocean island distribution function model according to claim 1, characterized in that: The steps to obtain parameters B and λ according to different fractal profiles are as follows: Step 2.1: Obtain parameters B and λ according to the fractal function; The relationship between number and diameter is obtained according to the algorithm, and the value of parameter B is obtained by fitting the data through the algorithm; According to the algorithm, the value of parameter λ at different heights is obtained, and at the same time, the value of parameter λ is calculated by taking different sampling lengths; The above results are obtained through algorithm calculation, and then the parameters B and λ are obtained, as shown in formula (6) and formula (7): In formula (6), B is the parameter to be determined, D is the fractal dimension, h is the cutoff height, h0 is the maximum distance between the island and the average height, l max represents the maximum island diameter, l represents the island diameter; According to formula (6), the parameter B is determined by the fractal dimension D and the cutoff height h; In formula (7), λ is the parameter to be determined, L represents the sampling length, L0 is the reference sampling length, h is the cutoff height, and h0 represents the maximum distance between the island and the average height; According to formula (7), the parameter λ is determined by the sampling length L and the cut-off height h: According to the numerical fitting, l max The changing law of is shown in formula (8): Formula (8) max represents the maximum island diameter, L0 is the reference sampling length, h is the cutoff height, h0 represents the maximum distance between the island and the average height, D is the fractal dimension, and a and b are parameters related to the fractal dimension; Therefore, the ocean island distribution function obtained by the WM function is: In formula (9), N is the number of ocean islands, and Λ is all islands larger than a certain island diameter; Step 2.2: Parameters B and λ obtained by Fourier transform; According to the algorithm, the value of parameter B is obtained, and at the same time, the value of parameter λ is obtained; The above results are calculated by the algorithm to obtain the parameters B and λ, as shown in formula (10) and formula (11): In formula (10), B is the parameter to be determined; According to formula (10), parameter B is determined by fractal dimension D and cutoff height h. In formula (11), λ is the parameter to be determined; According to formula (11), the parameter λ is determined by the cutoff height h, and l is obtained by numerical fitting. max The changing law of is shown in formula (12): Therefore, the ocean island distribution function obtained by Fourier transform method is: Step 2.3: Parameters B and λ are obtained based on experimental measurements of the fractal profile; According to the algorithm, the value of parameter B is obtained, and the value of parameter λ is calculated at the same time: According to the algorithm, the value of parameter λ under different sampling lengths is obtained; The above results are calculated by the algorithm to obtain the parameters B and λ, as shown in formula (14) and formula (15): According to formula (14), it is found that parameter B is determined by the fractal dimension D and the cutoff height h. In formula (15), Ra is the roughness; According to formula (15), it is found that the parameter λ is determined by the sampling length L and the cut-off height h; According to the numerical fitting, l max The change law of is shown in formula (16), where the roughness Ra is obtained according to actual measurement: Therefore, the ocean island distribution function obtained from the real machined surface is obtained; A new scale-dependent ocean island distribution function was obtained by theoretically and actually measuring the fractal profile of the processed specimens: In formula (18), F(L) is the function of the sampling length L, K(h / h0) is the function of h and h0, D is the fractal dimension, is a function of h and h0, ξ(l) is a function of the cutoff length; It can be seen from the above formula that for common fractal profiles, the ocean island distribution function has a unified structural form; where F(L) is the sampling length function, which is scale-related and proportional to the sampling length; for the fractal profile simulated by the WM function, F(L) = L / L0; for the fractal profile simulated by Fourier transform, F(L) = 1; for the machined surface, F(L) = 1.12L / (100Ra); K(h / h0) is the cutoff height function, which is parabolic with the cutoff height; for the fractal profile simulated by the WM function, K(h / h0) = 10 + 0.15(h / h0) - 11(h / h0) 2 ; For the fractal profile simulated by Fourier transform, K(h / h0)=6.8+0.15(h / h0)-6.54(h / h0) 2 ; For machined surfaces, K(h / h0)=8-0.5(h / h0)-10(h / h0) 2 ; is an exponentially truncated height function, a fractal profile simulated by the WM function For the fractal profile simulated by Fourier transform, For machined surfaces, ξ(l) is the cutoff length function. For the fractal profile simulated by the WM function, ξ(l) = 0.12(l max -l) / l max ; For the fractal profile simulated by Fourier transform, ξ(l)=0.15(l max -l) / l max ; For machined surfaces, ξ(l)=0.18(l max -l) / l max .

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